United went top with six points from two matches and a goal tally of 8-1 after second-half goals from Darren Fletcher, Louis Saha and substitute Ole Gunnar Solskjaer, his first for three years, sealed victory over bottom club Charlton at the Valley.
Chelsea, who beat Manchester City on Sunday, seemed set for a second consecutive win when Andriy Shevchenko put them 1-0 up on 16 minutes, his first league goal for the club following his move from AC Milan.
But late goals from Emanuel Pogatetz and Mark Viduka, in the last minute, gave hosts Boro a shock win.
"We know what pedigree they have and how hard you have to work to beat them and we did that tonight," said Gareth Southgate, who celebrated his first victory as Middlesbrough manager.
Chelsea manager Jose Mourinho was magnanimous in defeat, saying: "We only had ourselves to blame".
Aston Villa came from behind to beat promoted Reading 2-1 to give new manager Martin O'Neill victory on his Villa Park debut while Blackburn Rovers drew 1-1 with Everton.
Fulham drew 1-1 with Bolton Wanderers, both goals coming from penalties, and Manchester City drew 0-0 with Portsmouth, who had midfielder Pedro Mendes taken to hospital after being sent flying into the advertising hoardings by an elbow in the face from City defender Ben Thatcher.
Portsmouth are second on four points, the same total as West Ham United, Bolton, Aston Villa and Everton.
Wigan Athletic, who have only played one match, and Charlton, who have played twice, prop up the table with no points.